In this study we solved the issue of measuring the degree of overlap/segregation among an arbitrarily large number (n ≥ 2) of 3D volumetric home ranges (i.e., x, y, and hg; where hg is height above ground level) for the first time. For this purpose, we introduced the novel non-pairwise index MVOI (Multiple Volumetric Overlap Index) and its complement to 100 MVSI (Multiple Volumetric Segregation Index). Regardless of the number of 3D volumetric home ranges, the MVOI and MVSI generate a single score of overlap/segregation between 0 and 100, making ecological interpretation much easier and more meaningful when compared to n × n pairwise overlap indices. As a case study, we applied the MVOI and MVSI to 12,081 GPS points of five lesser kestrels (Falco naumanni) during the nesting period at Santeramo in Colle (Apulia region; Italy) in an area with the most elevated density of lesser kestrels in urban colonies worldwide. The 3D volumetric home ranges ranged between 1.79 km3 and 8.19 km3. We found that the tracked birds had different vertical profiles, possibly to limit intraspecific competition, resulting in a 3D home range overlap that was only 61.1% of the 2D overlap and 52.8% of the probabilistic one.
Keywords: 3D home range; 3D overlap/segregation estimator; animal space overlap; animal space use; biotelemetry; height above ground level; tessellation; topographic surface.